State The Principle Of Homogeneity Of Dimensions Test Class 11 ...

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AnswerQuestion Answers for Class 12Class 12 BiologyClass 12 ChemistryClass 12 EnglishClass 12 MathsClass 12 PhysicsClass 12 Social ScienceClass 12 Business StudiesClass 12 EconomicsQuestion Answers for Class 11Class 11 EconomicsClass 11 Computer ScienceClass 11 BiologyClass 11 ChemistryClass 11 EnglishClass 11 MathsClass 11 PhysicsClass 11 Social ScienceClass 11 AccountancyClass 11 Business StudiesQuestion Answers for Class 10Class 10 ScienceClass 10 EnglishClass 10 MathsClass 10 Social ScienceClass 10 General KnowledgeQuestion Answers for Class 9Class 9 General KnowledgeClass 9 ScienceClass 9 EnglishClass 9 MathsClass 9 Social ScienceQuestion Answers for Class 8Class 8 ScienceClass 8 EnglishClass 8 MathsClass 8 Social ScienceQuestion Answers for Class 7Class 7 ScienceClass 7 EnglishClass 7 MathsClass 7 Social ScienceQuestion Answers for Class 6Class 6 ScienceClass 6 EnglishClass 6 MathsClass 6 Social ScienceQuestion Answers for Class 5Class 5 ScienceClass 5 EnglishClass 5 MathsClass 5 Social ScienceQuestion Answers for Class 4Class 4 ScienceClass 4 EnglishClass 4 MathsState the principle of homogeneity of dimensions. Test the dimensional homogeneity of the following equation:\[\]$h = {h_0} + {v_0}t + \dfrac{1}{2}g{t^2}$AnswerVerified530.9k+ viewsHint- To solve this question we use the basic concept of dimension analysis. according to this; we can add and subtract only those quantities that have the same dimensions. For example we add three quantities ${h_0}$ , ${v_0}t$ and $\dfrac{1}{2}g{t^2}$ That means the dimensions of these all three are the same in this case.Complete step-by-step answer:Principle of Homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same. This principle is helpful because it helps us convert the units from one form to another. To better understand the principle, let us consider the following example:Testing the dimensional homogeneity for$h = {h_0} + {v_0}t + \dfrac{1}{2}g{t^2}$We have, As per dimensional Notation,h = ${\text{L}}$v = ${\text{L}}$${{\text{T}}^{{\text{ - 1}}}}$t = ${\text{T}}$g = ${\text{L}}$${{\text{T}}^{{\text{ - 2}}}}$The principle of homogeneity states that the dimensions of each the terms of a dimensional equation on both sides are the same. Using this principle, the given equation will have the same dimension on both sides.On left side: h=[L],On right hand side,RHS= ${\text{L}}$+ ${\text{[L}}{{\text{T}}^{{\text{ - 1}}}}{\text{AT] + }}\dfrac{{\text{1}}}{{\text{2}}}{\text{[L}}{{\text{T}}^{{\text{ - 2}}}}{\text{A}}{{\text{T}}^{\text{2}}}{\text{]}}$= ${\text{L}}$+ ${\text{L}}$+$\dfrac{1}{2}$[${\text{L}}$]= ${\text{L}}$Since All are of Dimension L , the result of sum is also equal to L.Therefore,LHS= RHS Dimensionally.So, the Relation is correct.Its application-The dimensional equations have got following uses:To check the correctness of a physical equation. To derive the relation between different physical quantities involved in a physical phenomenonTo change units from one system to anotherNote- Dimensional homogeneity is the concept where the dimensions of variables on both sides of an equation are the same. An equation could be dimensionally homogeneous but invalid if the equation is also not fully-balanced.Recently Updated PagesMaster Class 11 Computer Science: Engaging Questions & Answers for SuccessMaster Class 11 Business Studies: Engaging Questions & Answers for SuccessMaster Class 11 Economics: Engaging Questions & Answers for SuccessMaster Class 11 English: Engaging Questions & Answers for SuccessMaster Class 11 Maths: Engaging Questions & Answers for SuccessMaster Class 11 Biology: Engaging Questions & Answers for SuccessMaster Class 11 Computer Science: Engaging Questions & Answers for SuccessMaster Class 11 Business Studies: Engaging Questions & Answers for SuccessMaster Class 11 Economics: Engaging Questions & Answers for SuccessMaster Class 11 English: Engaging Questions & Answers for SuccessMaster Class 11 Maths: Engaging Questions & Answers for SuccessMaster Class 11 Biology: Engaging Questions & Answers for Success

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